Let's carefully analyze the given information and determine the recovery time for each person to choose the best answer.
1. Calculate the Total Cost of Education (Including Salary Loss During College):
For Person A:
- Salary prior to school: $18,000 per year
- Years attending college: 3 years
- Total cost of college: $45,000
The salary lost during college for Person A = 3 years [tex]$18,000 = $[/tex]54,000
The total cost for Person A = Salary lost during college + Total cost of college
= [tex]$54,000 + $[/tex]45,000 = $99,000
For Person B:
- Salary prior to school: $27,000 per year
- Years attending college: 4 years
- Total cost of college: $30,000
The salary lost during college for Person B = 4 years [tex]$27,000 = $[/tex]108,000
The total cost for Person B = Salary lost during college + Total cost of college
= [tex]$108,000 + $[/tex]30,000 = $138,000
2. Calculate the Additional Annual Salary Gain After College:
For Person A:
- Salary upon graduating: $33,000
- Salary prior to school: $18,000
Additional annual salary gain for Person A = [tex]$33,000 - $[/tex]18,000 = $15,000
For Person B:
- Salary upon graduating: $37,000
- Salary prior to school: $27,000
Additional annual salary gain for Person B = [tex]$37,000 - $[/tex]27,000 = $10,000
3. Calculate the Recovery Time for Each Person:
For Person A:
- Total cost of education: $99,000
- Additional annual salary gain: $15,000
Recovery time for Person A = Total cost of education / Additional annual salary gain
= [tex]$99,000 / $[/tex]15,000 = 6.6 years
For Person B:
- Total cost of education: $138,000
- Additional annual salary gain: $10,000
Recovery time for Person B = Total cost of education / Additional annual salary gain
= [tex]$138,000 / $[/tex]10,000 = 13.8 years
Based on these calculations, Person A recovers their investment in 6.6 years, whereas Person B takes 13.8 years to recover their investment.
Therefore, the best answer is:
a. Person A recovers their investment in a shorter amount of time.
